Dictionaries, Hash Tables and Sets

1. Dictionaries, Hash Tables and Sets Dictionaries, Hash Tables, Hashing, Collisions, Sets Data Structures and Algorithms Telerik Software Academy http://academy.telerik.com

2. Table of Contents • Dictionaries • Hash Tables • Dictionary<TKey,TValue> Class • Sets: HashSet<T> and SortedSet<T>

3. Dictionaries Data Structures that Map Keys to Values

4. The Dictionary (Map) ADT • The abstract data type (ADT) "dictionary" maps key to values • Also known as "map" or "associative array" • Contains a set of (key, value) pairs • Dictionary ADT operations: • Add(key,value) • FindByKey(key)value • Delete(key) • Can be implemented in several ways • List, array, hash table, balanced tree, ...

5. ADT Dictionary – Example • Example dictionary:

6. Hash Tables What is Hash Table? How it Works?

7. Hash Table • A hash table is an array that holds a set of(key, value) pairs • The process of mapping a key to a positionin a table is called hashing T h(k) Hash function h:k→0…m-1 Hash table of size m

8. Hash Functions and Hashing • A hash table has m slots, indexed from 0 to m-1 • A hash function h(k) maps keys to positions: • h:k → 0…m-1 • For any value k in the key range and some hash function h we have h(k)=p and 0≤p<m T h(k)

9. Hashing Functions • Perfect hashing function (PHF) • h(k) : one-to-one mapping of each key k to an integer in the range [0,m-1] • The PHF maps each key to a distinct integer within some manageable range • Finding a perfect hashing function is in most cases impossible • More realistically • Hash function h(k)that maps most of the keys onto unique integers, but not all

10. Collisions in a Hash Table • A collision is the situation when different keys have the same hash value h(k1)=h(k2)fork1≠k2 • When the number ofcollisions is sufficiently small, the hash tables work quite well (fast) • Several collisions resolution strategies exist • Chaining in a list • Using the neighboring slots (linear probing) • Re-hashing (second hash function) • ...

11. Collision Resolution: Chaining h("Pesho") = 4 h("Kiro") = 2 h("Mimi") = 1 h("Ivan") = 2 h("Lili") = m-1 Chaining elements in case of collision collision T Mimi Kiro Pesho Lili Ivan null null null null

12. Hash Tables and Efficiency • Hash tables are the most efficient implementation of ADT "dictionary" • Add / Find / Delete take just few primitive operations • Speed does not depend on the size of the hash-table (constant time) • Amortized complexity O(1) • Example: finding an element in a hash-table with 1 000 000 elements, takes just few steps • Finding an element in array of 1 000 000 elements takes average 500 000 steps

13. Dictionaries: .NET Interfaces and Implementations

14. Hash Tables in C# The Dictionary<TKey,TValue> Class

15. Dictionary<TKey,TValue> • Implements the ADT dictionary as hash table • The size is dynamically increased as needed • Contains a collection of key-value pairs • Collisions are resolved by chaining • Elements have almost random order • Ordered by the hash code of the key • Dictionary<TKey,TValue> relies on • Object.Equals()– for comparing the keys • Object.GetHashCode()– for calculating the hash codes of the keys

16. Dictionary<TKey,TValue> (2) • Major operations: • Add(TKey,TValue)– adds an element with the specified key and value • Remove(TKey)– removes the element by key • this[] – get / add / replace of element by key • Clear()– removes all elements • Count – returns the number of elements • Keys – returns a collection of the keys • Values – returns a collection of the values

17. Dictionary<TKey,TValue> (3) • Major operations: • ContainsKey(TKey)– checks whether the dictionary contains given key • ContainsValue(TValue) – checks whether the dictionary contains given value • Warning: slow operation – O(n) • TryGetValue(TKey,outTValue) • If the key is found, returns it in the TValue • Otherwise returns false

18. Dictionary<TKey,TValue> – Example Dictionary<string, int> studentsMarks = new Dictionary<string, int>(); studentsMarks.Add("Ivan", 4); studentsMarks.Add("Peter", 6); studentsMarks.Add("Maria", 6); studentsMarks.Add("George", 5); int peterMark = studentsMarks["Peter"]; Console.WriteLine("Peter's mark: {0}", peterMark); Console.WriteLine("Is Peter in the hash table: {0}", studentsMarks.ContainsKey("Peter")); Console.WriteLine("Students and grades:"); foreach (var pair in studentsMarks) { Console.WriteLine("{0} --> {1}", pair.Key, pair.Value); }

19. Dictionary<TKey,TValue> Live Demo

20. Counting the Words in a Text string text = "a text, some text, just some text"; IDictionary<string, int> wordsCount = new Dictionary<string, int>(); string[] words = text.Split(' ', ',', '.'); foreach (string word in words) { int count = 1; if (wordsCount.ContainsKey(word)) count = wordsCount[word] + 1; wordsCount[word] = count; } foreach(var pair in wordsCount) { Console.WriteLine("{0} -> {1}", pair.Key, pair.Value); }

21. Counting the Words in a Text Live Demo

22. Nested Data Structures • Data structures can be nested, e.g. dictionary of lists: Dictionary<string,List<int>> static Dictionary<string, List<int>> studentGrades = new Dictionary<string, List<int>>(); private static void AddGrade(string name, int grade) { if (! studentGrades.ContainsKey(name)) { studentGrades[name] = new List<int>(); } studentGrades[name].Add(grade); }

23. Dictionary of Lists Live Demo

24. Balanced Tree Dictionaries The SortedDictionary<TKey,TValue> Class

25. SortedDictionary<TKey,TValue> • SortedDictionary<TKey,TValue> implements the ADT "dictionary" as self-balancing search tree • Elements are arranged in the tree ordered by key • Traversing the tree returns the elements in increasing order • Add / Find / Delete perform log2(n) operations • Use SortedDictionary<TKey,TValue> when you need the elements sorted by key • Otherwise use Dictionary<TKey,TValue> – it has better performance

26. Counting Words (Again) string text = "a text, some text, just some text"; IDictionary<string, int> wordsCount = new SortedDictionary<string, int>(); string[] words = text.Split(' ', ',', '.'); foreach (string word in words) { int count = 1; if (wordsCount.ContainsKey(word)) count = wordsCount[word] + 1; wordsCount[word] = count; } foreach(var pair in wordsCount) { Console.WriteLine("{0} -> {1}", pair.Key, pair.Value); }

27. Counting the Words in a Text Live Demo

28. Comparing Dictionary Keys Using custom key classes in Dictionary<TKey, TValue> and SortedDictionary<TKey,TValue>

29. IComparable<T> • Dictionary<TKey,TValue> relies on • Object.Equals() – for comparing the keys • Object.GetHashCode()– for calculating the hash codes of the keys • SortedDictionary<TKey,TValue> relies on IComparable<T> for ordering the keys • Built-in types like int, long, float, string and DateTime already implement Equals(), GetHashCode() and IComparable<T> • Other types used when used as dictionary keys should provide custom implementations

30. Implementing Equals() and GetHashCode() public struct Point { public int X { get; set; } public int Y { get; set; } public override bool Equals(Object obj) { if (!(obj is Point) || (obj == null)) return false; Point p = (Point)obj; return (X == p.X) && (Y == p.Y); } public override int GetHashCode() { return (X << 16 | X >> 16) ^ Y; } }

31. Implementing IComparable<T> public struct Point : IComparable<Point> { public int X { get; set; } public int Y { get; set; } public int CompareTo(Point otherPoint) { if (X != otherPoint.X) { return this.X.CompareTo(otherPoint.X); } else { return this.Y.CompareTo(otherPoint.Y); } } }

32. Sets Sets of Elements

33. Set and Bag ADTs • The abstract data type (ADT) "set" keeps a set of elements with no duplicates • Sets with duplicates are also known as ADT "bag" • Set operations: • Add(element) • Contains(element)true / false • Delete(element) • Union(set) / Intersect(set) • Sets can be implemented in several ways • List, array, hash table, balanced tree, ...

34. Sets: .NET Interfacesand Implementations

35. HashSet<T> • HashSet<T> implements ADT set by hash table • Elements are in no particular order • All major operations are fast: • Add(element) – appends an element to the set • Does nothing if the element already exists • Remove(element) – removes given element • Count – returns the number of elements • UnionWith(set) / IntersectWith(set) – performs union / intersection with another set

36. HashSet<T> – Example ISet<string> firstSet = new HashSet<string>( new string[] { "SQL", "Java", "C#", "PHP" }); ISet<string> secondSet = new HashSet<string>( new string[] { "Oracle", "SQL", "MySQL" }); ISet<string> union = new HashSet<string>(firstSet); union.UnionWith(secondSet); PrintSet(union); // SQL Java C# PHP Oracle MySQL private static void PrintSet<T>(ISet<T> set) { foreach (var element in set) { Console.Write("{0} ", element); } Console.WriteLine(); }

37. SortedSet<T> • SortedSet<T> implements ADT set by balanced search tree (red-black tree) • Elements are sorted in increasing order • Example: ISet<string> firstSet = new SortedSet<string>( new string[] { "SQL", "Java", "C#", "PHP" }); ISet<string> secondSet = new SortedSet<string>( new string[] { "Oracle", "SQL", "MySQL" }); ISet<string> union = new HashSet<string>(firstSet); union.UnionWith(secondSet); PrintSet(union); // C# Java PHP SQL MySQL Oracle

38. HashSet<T> and SortedSet<T> Live Demo

39. Summary • Dictionaries map key to value • Can be implemented as hash table or balanced search tree • Hash-tables map keys to values • Rely on hash-functions to distribute the keys in the table • Collisions needs resolution algorithm (e.g. chaining) • Very fast add / find / delete – O(1) • Sets hold a group of elements • Hash-table or balanced tree implementations

40. Dictionaries, Hash Tables and Sets http://academy.telerik.com

41. Exercises • Write a program that counts in a given array of double values the number of occurrences of each value. Use Dictionary<TKey,TValue>. Example: array = {3, 4, 4, -2.5, 3, 3, 4, 3, -2.5} -2.52 times 34 times 4 3 times • Write a program that extracts from a given sequence of strings all elements that present in it odd number of times. Example: {C#, SQL, PHP, PHP, SQL, SQL }  {C#, SQL}

42. Exercises (2) • Write a program that counts how many times each word from given text file words.txt appears in it. The character casing differences should be ignored. The result words should be ordered by their number of occurrences in the text. Example: is  2 the  2 this  3 text  6 This is the TEXT. Text, text, text – THIS TEXT! Is this the text?

43. Exercises (3) • Implement the data structure "hash table" in a class HashTable<K,T>. Keep the data in array of lists of key-value pairs (LinkedList<KeyValuePair<K,T>>[]) with initial capacity of 16. When the hash table load runs over 75%, perform resizing to 2 times larger capacity. Implement the following methods and properties: Add(key,value), Find(key)value, Remove( key), Count, Clear(), this[], Keys. Try to make the hash table to support iterating over its elements with foreach. • Implement the data structure "set" in a class HashedSet<T> using your class HashTable<K,T> to hold the elements. Implement all standard set operations like Add(T), Find(T), Remove(T), Count, Clear(), union and intersect.

44. Exercises (4) • * A text file phones.txt holds information about people, their town and phone number: Duplicates can occur in people names, towns and phone numbers. Write a program to read the phones file and execute a sequence of commands given in the file commands.txt: • find(name) – display all matching records by given name (first, middle, last or nickname) • find(name,town) – display all matching records by given name and town Mimi Shmatkata | Plovdiv | 0888 12 34 56 Kireto | Varna | 052 23 45 67 Daniela Ivanova Petrova | Karnobat | 0899 999 888 Bat Gancho | Sofia | 02 946 946 946

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